Defining parameters
| Level: | \( N \) | = | \( 242 = 2 \cdot 11^{2} \) |
| Weight: | \( k \) | = | \( 6 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Sturm bound: | \(21780\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(242))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 9235 | 2975 | 6260 |
| Cusp forms | 8915 | 2975 | 5940 |
| Eisenstein series | 320 | 0 | 320 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(242))\)
We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
| Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
|---|---|---|---|---|
| 242.6.a | \(\chi_{242}(1, \cdot)\) | 242.6.a.a | 1 | 1 |
| 242.6.a.b | 1 | |||
| 242.6.a.c | 1 | |||
| 242.6.a.d | 1 | |||
| 242.6.a.e | 1 | |||
| 242.6.a.f | 2 | |||
| 242.6.a.g | 2 | |||
| 242.6.a.h | 2 | |||
| 242.6.a.i | 3 | |||
| 242.6.a.j | 3 | |||
| 242.6.a.k | 4 | |||
| 242.6.a.l | 4 | |||
| 242.6.a.m | 4 | |||
| 242.6.a.n | 4 | |||
| 242.6.a.o | 6 | |||
| 242.6.a.p | 6 | |||
| 242.6.c | \(\chi_{242}(3, \cdot)\) | n/a | 180 | 4 |
| 242.6.e | \(\chi_{242}(23, \cdot)\) | n/a | 550 | 10 |
| 242.6.g | \(\chi_{242}(5, \cdot)\) | n/a | 2200 | 40 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(242))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(242)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)